https://arxiv.org/abs/2302.03389
Abstract: Quantum Machine Learning is the field that aims to integrate Machine Learning into quantum computation. Recently, some works have shown that we can naturally generate one-dimensional Fourier series with a supervised quantum machine learning model. However, models used for multi-dimensional Fourier series have not been explored with the same level of detail. In this work, we study different quantum strategies for fitting arbitrary multi-dimensional Fourier series. Using different types of circuit ansatzes, we found that the degrees of freedom required for fitting such functions grow faster than the degrees disposed of in the Hilbert space generated by the circuit. These results exhibit that, for these types of problems, the model does not have enough freedom to achieve any arbitrary Fourier series. Our work contributes to the study of multi-feature quantum machine learning algorithms with classical data and concludes that new encoding strategies beyond Fourier series formalism could be more convenient.
In this repository you will find the code to reproduce the simulations on the article "Multi-dimensional Fourier series with quantum circuits" for fitting two-dimensional functions. The file "ansatzes_2_qubits.ipynb" contains two ciruit models, the Line and Parallel Ansatzes. There are two classes, one named fitting_qubit, for the Line Ansatz, and other fitting_qubits, for the Parallel Ansatz. Each one contains the definition of the quantum gates used, the quantum circuit, the cost function, the optimization method and the code for the plots. The file is designed for fitting a two-dimensional target function.